Friday, September 04, 2009

Another Anscombe
Something completely different

When I read the phrase Anscombe's quartets, I thought of the mighty GEM herself, but this is brilliant:  4 datasets with the same x,y mean and variance, the same regression line and the same correlation coefficient, but with completely different properties that are obvious as soon as you graph them. Suitably modified, this would make a lovely introduction to practical work for 1st year undergraduates: if nothing else, it might get them away from bunging the data into excel and plotting a regression line without graphing them first. Hmmmm.


pj said...

In my old field of research I was always amazed at the way people used linear corrections (usually multivariate) without ever looking at the graphed data. Generally it seems like you just end up with semi-nonsensical numbers but it was just the way things were done.

Political Scientist said...

Ah, but were they publishable nonsensical numbers :)

I would wager at least modest sums there are certain people in the physics community who would claim that the curved data set, plotted on a log-log scale, was evidence of a power law. In fact, for my hypothetical 1st year problem sheet, I'd make them plot the data on a log-log scale to show that practically everything looks like a straight line if plotted on a log-log scale with suitably chosen limits.